Differential inclusions with mean derivatives, having aspherical right-hand sides

Yu. E. Gliklikh

Čebyševskij sbornik, Tome 21 (2020) no. 2, pp. 84-93.

Résumé

On flat $ n $-dimensional torus we study stochastic differential inclusions with mean derivatives, for which the right-hand sides have, generally speaking, not convex (aspherical) values. A subclass of such inclusions is distinguished for which there exists a sequence of $\varepsilon$-approximations, converging point-wise to a Borel measurable selector. On this base a solution existence theorem is obtained.

Détail

Keywords: mean derivatives, differential inclusions, aspherical right-hand sides, point-wise convergence, solution existence.

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